Exponential Equations and Functions

This video tutorial explains how to solve exponential equations by rewriting both sides to have the same base. The method involves setting the exponents equal and solving the resulting equation. The video demonstrates this process with an example, showing how to rewrite 125 as a power of 5 and solve for the variable. It emphasizes the importance of checking the solution by substituting it back into the original equation. The tutorial concludes by mentioning that logarithms are needed if the bases cannot be rewritten to be the same.

What is the first step in solving an exponential equation by rewriting both sides to have the same base?

• Add the exponents together.

• Rewrite both sides to have the same base.

• Divide both sides by the base.

• Use logarithms to simplify the equation.

In an exponential equation, what does the base refer to?

• The result of the equation.

• The number being multiplied by the exponent.

• The sum of the exponents.

• The variable in the equation.

What is the base in the equation 5^x = 125?

• 125

• 5

• x

• 3

What is the exponent in the equation 5^x = 125?

• x

• 3

• 5

• 125

How can 125 be rewritten as a power of 5?

• 5^2

• 5^3

• 5^4

• 5^5

What is the result of 5 times 5?

• 10

• 20

• 25

• 15

What is the result of 25 times 5?

• 175

• 150

• 125

• 100

What should you do after rewriting both sides of the equation to have the same base?

• Subtract the exponents.

• Multiply the exponents.

• Set the exponents equal to each other.

• Add the exponents together.

What is the solution to the equation 2x + 1 = 3?

• x = 3

• x = 2

• x = 1

• x = 0

What is the purpose of setting the exponents equal to each other?

• To find the base.

• To solve for the variable.

• To change the base.

• To simplify the equation.